and even more so if it runs in the cloud (just use an EMP).

The point was that you can't use an EMP if that means bringing down the whole human computer network.

t isn't trivial. There is a strong interdependence of resources and manufacturers. The AI won't be able to simply make some humans build a high-end factory to create computational substrate. People will ask questions and shortly after get suspicious.

Why would people need to get suspicious? If you have tabs on all the communications in the world, you can make a killing on the market, even if you didn't delay the orders from your competitors. One could fully legitimately raise enough money by trading to hire people to do everything you wanted. Nobody needs to ever notice that there's something amiss, especially not if you do it via enough shell corporations.

Of course, the AGI could also use more forceful means, though it's by no means necessary. If the AGI revealed itself and the fact that it was holding all of humanity's networked computers hostage, it could probably just flat-out tell the humans "do this or else". Sure, not everyone would obey, but some would. Also, disrupt enough communications and manufacture enough chaos, and people will be too distracted and stressed to properly question forged orders. Social engineering is rather easy with humans, and desperate people are quite prone to wishful thinking.

Remember it won't be able to coordinate a world-conspiracy because it hasn't been able to self-improve to that point yet because it is still trying to acquire enough resources which it has to do the hard way without nanotech.

This claim strikes me as bizarre. Why would you need nanotech to acquire more resources for self-improvement?

Some botnets have been reported to have around 350,000 members. Currently, the distributed computing project Folding@Home, with 290,000 active clients composed mostly of volunteer home PCs and Playstations, can reach speeds in the 10^15 FLOPS range. Now say that an AGI gets developed in 20 years from now. A relatively conservative estimate that presumed an AGI couldn't hack into more computers than the best malware practicioners of today, that a personal computer would have a hundred times the computing power of today, and that an AGI required a minimum of 10^13 FLOPS to run, would suggest that an AGI could either increase its own computational capacity 12,000-fold, or spawn 12,000 copies of itself.

Alternatively, if it wanted to avoid detection and didn't want to do anything illegal or otherwise suspicious, it could just sign up on a site like oDesk and do lots of programming jobs for money, then rent all the computing capacity it needed until it was ready to unleash itself to the world. This is actually the more likely alternative, as unlike the botnet/hacking scheme it's a virtually risk-free to gain extra processing power.

Acquiring computational resources is easy, and it will only get easier as time goes on. Also, while upgrading your hardware is one way of self-improving, you seem to be completely ignoring the potential for software self-improvement. It's not a given that the AGI would even need massive hardware. For instance:

Grötschel, an expert in optimization, observes that a benchmark production planning model solved using linear programming would have taken 82 years to solve in 1988, using the computers and the linear programming algorithms of the day. Fifteen years later – in 2003 – this same model could be solved in roughly 1 minute, an improvement by a factor of roughly 43 million. Of this, a factor of roughly 1,000 was due to increased processor speed, whereas a factor of roughly 43,000 was due to improvements in algorithms! Grötschel also cites an algorithmic improvement of roughly 30,000 for mixed integer programming between 1991 and 2008.